Measurements of the expansion rate of the Universe based on a Hubble diagram of QSOs combined with SNe Ia show a deviation from the concordance model at high redshifts (\(z>1.4\) ), with a statistical significance of \(\sim 3-4\sigma \)  [1]}. Figure REF  presents the Hubble diagram for the most up-to-date samples of QSOs [2]} and SNe Ia from the Pantheon survey [3]}.
The best cosmographic fit (performed through a Monte Carlo Markov Chain analysis) is shown with the red line [4]}, whilst black points are the means (along with the uncertainty on the mean) of the distance modulus in narrow (logarithmic) redshift intervals, plotted for clarity purposes only.
It is evident from this figure the potential of QSOs to extend the distance modulus-redshift relation in a cosmic epoch (\(z>2\) ) that it is poorly sampled by any other cosmological probe. QSOs are indeed key to discriminate amongst various cosmological models that are instead degenerate at low redshifts, and to improve the constraints on a possible evolution of the dark energy parameter with time.
Additional data are required at high redshifts where very few QSOs are available with both X-ray and UV observations that fulfil the selection criteria discussed in section REF .
